Long Views: X-Prize Foundation's Peter Diamandis has led an unusual charge:

With the help of Google, the X Prize became a foundation to generate aseries of competitions for 'audacious and achievable goals.' The
attributes for a good Prize competition are: very large cash prize;
clear objective and simple rules; a defined problem rather than defined
solution; a target that had become stuck; something that attracts
maverick thinkers; something whose success will change people’s sense
of what is possible.

Now, according to Stewart Brand, who blogged Diamandis speaking at a Long Now Foundation seminar last Friday, Diamandis suggests something even bigger, Mega-X Prizes:

They would have a purse of $100 million to $1 billion. (Not
implausible; there are 1,200 billionaires in the world now.) As an
example of how the economics could make sense, Diamandis points out
that the current cost of AIDS is $80 billion a year, $800 billion a
decade. A successful $1 billion X Prize for a cure for AIDS would be a
hugely efficient economic event as well as a massive humanitarian
breakthrough.

Brand lists 35 such proposals, including faster-than-light communications, instruments that can detect cancer at the 100-cell stage "and zap it," and the first human on Mars.